/**
 * @file methods/ann/dists/normal_distribution_impl.hpp
 * @author xiaohong ji
 * @author Nishant Kumar
 *
 * Implementation of the Normal Distribution class.
 *
 * mlpack is free software; you may redistribute it and/or modify it under the
 * terms of the 3-clause BSD license.  You should have received a copy of the
 * 3-clause BSD license along with mlpack.  If not, see
 * http://www.opensource.org/licenses/BSD-3-Clause for more information.
 */
#ifndef MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_IMPL_HPP
#define MLPACK_METHODS_ANN_DISTRIBUTIONS_NORMAL_DISTRIBUTION_IMPL_HPP

// In case it hasn't yet been included.
#include "normal_distribution.hpp"

namespace mlpack {
namespace ann /** Artificial Neural Network. */ {

template<typename DataType>
NormalDistribution<DataType>::NormalDistribution()
{
  // Nothing to do here.
}

template<typename DataType>
NormalDistribution<DataType>::NormalDistribution(
    const DataType& mean,
    const DataType& sigma) :
    mean(mean),
    sigma(sigma)
{
  // Nothing to do here.
}

template<typename DataType>
DataType NormalDistribution<DataType>::Sample() const
{
  return sigma * arma::randn<DataType>(mean.n_elem) + mean;
}

template<typename DataType>
DataType NormalDistribution<DataType>::LogProbability(
    const DataType& observation) const
{
  const DataType v1 = arma::log(sigma) + std::log(std::sqrt(2 * M_PI));
  const DataType v2 = arma::square(observation - mean) /
                      (2 * arma::square(sigma));
  return  (-v1 - v2);
}

template<typename DataType>
void NormalDistribution<DataType>::ProbBackward(
    const DataType& observation,
    DataType& dmu,
    DataType& dsigma) const
{
  dmu = (observation - mean) / (arma::square(sigma)) % Probability(observation);
  dsigma = (- 1.0 / sigma +
            (arma::square(observation - mean) / arma::pow(sigma, 3)))
            % Probability(observation);
}

template<typename DataType>
template<typename Archive>
void NormalDistribution<DataType>::serialize(Archive& ar,
                                             const unsigned int /* version */)
{
  ar & BOOST_SERIALIZATION_NVP(mean);
  ar & BOOST_SERIALIZATION_NVP(sigma);
}

} // namespace ann
} // namespace mlpack

#endif